Abstract The idea that the stress-strain curve satisfies different ordinary differential equations in its different segment is proposed and implemented. In contrast to the classical Ramberg-Osgood law, the model establishes the dependence of stress on deformation. For each segment of the deformation curve, a differential equation is formulated that corresponds to the physics of deformation in this section. The curve is divided into two segment: linear and nonlinear. In the first segment, a second-order differential equation of the simplest type is postulated. In the second segment, a fourth-order differential equation is postulated. The boundary value problem in each segment is formulated from the requirement of continuity and differentiability of the deformation curve. The resulting solution has the advantage that, in contrast to the empirical Ramberg-Osgood law, it has a strictly linear part of the stress-strain curve. The proposed model was tested on modeling the elastoplastic properties of four Russian steels. The standard deviation of the theoretical curves from the samples of the experimental points did not exceed 2.5% for all materials.

中文翻译：

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作为四阶微分方程解的非线性应力-应变曲线模型

摘要 提出并实现了应力-应变曲线在其不同段满足不同常微分方程的思想。与经典的 Ramberg-Osgood 定律相反，该模型建立了应力对变形的依赖性。对于变形曲线的每一段，都制定了一个微分方程，对应于本节中的变形物理。曲线分为两段：线性和非线性。在第一段中，假设了最简单类型的二阶微分方程。在第二段中，假设了一个四阶微分方程。从变形曲线的连续性和可微性的要求出发，制定了各段边值问题。由此产生的解决方案的优点是，与经验 Ramberg-Osgood 定律相反，它具有应力-应变曲线的严格线性部分。所提出的模型在模拟四种俄罗斯钢的弹塑性特性时进行了测试。对于所有材料，来自实验点样品的理论曲线的标准偏差不超过 2.5%。